A Simultaneous Parametric Maximum-Flow Algorithm for Finding the Complete Chain of Solutions
نویسندگان
چکیده
A Simultaneous Parametric Maximum-flow (SPM) algorithm finds the maximum-flow and a min-cut of a bipartite parametric maximum-flow network simultaneously for all values of parameter . λ Instead of working with the original parametric network, a new network is derived from the original and the SPM gives a particular state of the flows in the derived network, from which the nested min-cuts under all lambda values is derived in a single scan of the nodes in a sorted order. All breakpoints of λ where the maximum-flow as a step-function of λ jumps is discovered by the SPM. The maximum flows at these λ -values are calculated in O(m) time from the min-cuts; m is the number of arcs. Generalization beyond bipartite networks is also shown.
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